论文标题
模块化形式，穿刺球的变形以及对称张量表示的扩展
Modular forms, deformation of punctured spheres, and extensions of symmetric tensor representations
论文作者
论文摘要
令〜$ x = \ po/γ$为一个〜$ n $ pundust的球体，$ n> 3 $。我们根据均匀化的微分方程和附件参数的经典理论介绍和研究〜$ n-3 $变形操作员〜$ m _*（γ）$。在限制模块化函数时，我们在Teichmüller理论中恢复了与〜$ x $的复杂结构的变形有关的构造。我们用衍生物来描述相对于重量四尖的Eichler积分以及与对称张量表示的扩展相关的矢量值模块形式的变形算子。
Let~$X=\Po/Γ$ be an~$n$-punctured sphere, $n>3$. We introduce and study~$n-3$ deformation operators on the space of modular forms~$M_*(Γ)$ based on the classical theory of uniformizing differential equations and accessory parameters. When restricting to modular functions, we recover a construction in Teichmüller theory related to the deformation of the complex structure of~$X$. We describe the deformation operators in terms of derivations with respect to Eichler integrals of weight-four cusp forms, and in terms of vector-valued modular forms attached to extensions of symmetric tensor representations.
